clifford.BasisVectorIds

class clifford.BasisVectorIds(blade_ids: Sequence[IdT])

Stores ids for the ordered set of basis vectors, typically integers.

Provides helpers to convert between bitmaps indicating which vectors are present in a blade, and tuples of the original ids.

For example:

>>> ids = BasisVectorIds([11, 22, 33])
>>> ids.bitmap_as_tuple(0b110)
(22, 33)
>>> sign, bitmap = ids.tuple_as_sign_and_bitmap((33, 22))
>>> assert sign, bitmap == (-1, 0b110)

bitmap_as_tuple(bitmap: int) → Tuple[IdT]

Convert a bitmap representation into a tuple of ids.

id_as_bitmap(id: IdT) → int

Convert the id of a single vector into a bitmap representation.

tuple_as_sign_and_bitmap(blade: Tuple[IdT]) → Tuple[int, int]

Convert a blade from a tuple of ids into a bitmap representation.

order_from_tuples(blades: Sequence[Tuple[IdT]]) → BasisBladeOrder

Produce an ordering from a set of tuples.

This is the inverse of order_as_tuples().

>>> ids = BasisVectorIds(['x', 'y'])
>>> ids.order_from_tuples([(), ('y',), ('x', 'y'), ('x',)])
BasisBladeOrder([0b00, 0b10, 0b11, 0b01])

order_as_tuples(ordering: BasisBladeOrder) → List[Tuple[IdT]]

Represent an ordering with these ids.

This is the inverse of order_from_tuples().

>>> ids = BasisVectorIds(['x', 'y'])
>>> ids.order_as_tuples(BasisBladeOrder([0b00, 0b10, 0b11, 0b01]))
[(), ('y',), ('x', 'y'), ('x',)]

classmethod ordered_integers(n: int, *, first_index: int = 1) → BasisVectorIds[int]

Create a set of n sequential integers as ids, starting from first_index.

augmented_with(n: int) → BasisVectorIds

Return a new copy with n new ids at the end.